The Big Bang Theory Season 10 Episode 18
The Escape Hatch Identification
Raj has to move out of his apartment because of his financial troubles, and both Howard and Bernadette and Leonard and Penny offer him a place to stay. Raj decides to move in with Leonard and Penny, and take Sheldon's old room.
Sheldon feels conflicted about the fact that someone else will be living in his room, and he video chats with Leonard's mom to get some help understanding why. She suggests he thinks of his old room as an escape hatch -- a way to exit his relationship with Amy if he needs to.
She also mentions that it says something about Leonard and Penny's relationship that they've decided to take on a new roommate.
Penny and Leonard argue because of that revelation, and they worry if there's an issue. They also talk about the fact that Penny tried to get her brother to move in with them as well.
Raj becomes uncomfortable, and he decides to leave and stay with Howard and Bernadette. Stuart tells Raj how great it is living with Howard and Bernadette, but Raj worries about being a burden. Leonard and Penny convince him to come back and that he won't cause problems for them.